A (new) prime theorem.

[troels munkner]

"A Prime Number Theorem" was published in 1986
(ISBN 87 7245 129 7, Rhodos Publishers Copenhagen, DK).

"Possible primes" were defined as [(6*m)+1], m being an integer
from - infinity to + infinity.
Negative possible primes (-5,-11,-17,-23.....) have modules V, II or VIII.
Positive possible primes (1,7,13,19,25,....) have modules I, VII or IV.

The integers 2 and 3 cannot be defined as possible primes (6*m +1)
and should not be considered as primes.

The integer 1 is a square (6*0 +1)*(6*0 +1), just as 25 is equal to
[(6*(-1) +1)] * [(6*(-1) +1)]
and 49 is equal to [(6*(+1) +1)] * [(6*(+1) +1)].

Products of possible primes remain possible primes
36 * (n*m) + 6* (n+m) +1, n being an integer from - infinity to + infinity.

All Mersenne primes are positive possible primes and will be defined
in a later thread.

Troels Munkneer

]

[Mini-Geek]

Originally Posted by troels munkner

The integers 2 and 3 cannot be defined as possible primes (6*m +1)
and should not be considered as primes.

Are you saying that 2 and 3 are not prime and are therefore composite? Do you happen to know of an integer that divides either of them besides 1?

Originally Posted by troels munkner

[(6*(+1) +1)] * [(6*(+1) +1)].

The syntax of this is incorrect. You cannot say (+1), it is just plain incorrect. What do you mean by this?

[retina]

Originally Posted by troels munkner

All Mersenne primes are positive possible primes

For all n=odd, n>=1 the following will hold ((2^n)-1)=6m+1. But what does that prove? What are you trying to say?

[Jens K Andersen]

troels munkner doesn't follow standard definitions and conventions, and his work is not supported by others.
I suggest moving this thread to Miscellaneous Math Threads. If I were a moderator, I would ask him to only post about his "possible primes" there. Maybe merge this thread with some of his similar unsupported stuff here or here. And delete his duplicate post in Information & Answers.

[ewmayer]

Originally Posted by troels munkner

"A Prime Number Theorem" was published in 1986
(ISBN 87 7245 129 7, Rhodos Publishers Copenhagen, DK).

If that is true, and APNT is basically the same bogus crap you keep posting to this board every few months, it seems their editorial standards are "colossally" low.

The integers 2 and 3 cannot be defined as possible primes (6*m +1)
and should not be considered as primes.

You have a most curious definition of "possible prime." Note that I do not intend "curious" to imply in any way that your "definition" is interesting - rather, the kinds of descriptive terms that do come to mind include "idiotic," "clueless", and "wasteful of other people's time." Might I suggest that you either keep your inane musings to yourself, or take them elsewhere? I normally would refrain from using such harsh language, but this is not the first time you've posted this garbage here.

The integer 1 is a square (6*0 +1)*(6*0 +1), just as 25 is equal to
[(6*(-1) +1)] * [(6*(-1) +1)]
and 49 is equal to [(6*(+1) +1)] * [(6*(+1) +1)].

And this tells us what, exactly? That certain perfect squares are ... perfect squares?

Products of possible primes remain possible primes
36 * (n*m) + 6* (n+m) +1, n being an integer from - infinity to + infinity.

So the primes 2 and 3 are in fact not prime, at the same time that any product of your designated 6k+1 possible primes is not clearly composite? You sir, are a moron.

All Mersenne primes are positive possible primes and will be defined
in a later thread.

I tremble at the thought of the further "enlightenment" you speak of.

[troels munkner]

Originally Posted by Jens K Andersen

troels munkner doesn't follow standard definitions and conventions, and his work is not supported by others.
I suggest moving this thread to Miscellaneous Math Threads. If I were a moderator, I would ask him to only post about his "possible primes" there. Maybe merge this thread with some of his similar unsupported stuff here or here. And delete his duplicate post in Information & Answers.

a polite dialogue will be appreciated
All integers from - infinity to + infinity can be subdivided into three groups.
A. Even integers which will be products of 2 and an other integer.
B. Odd integers divisible by 3 which will be products of 3 and an other
odd integer.
C. Odd integers which are not divisible by 3.
Their general form is (6*m +1), m being an integer from - infinity
to + infinity.
These integers can be grouped as "possible primes" and comprise
real primes and possible prime products.
All possible primes are "located" along a straight line wuith an individual
difference of 6, i.e. (6*m +1) --- (-35), (-29), (-23), (-17), (-11), (-5),
1,7,13,19,25,31,37 --- (6*m +1)
Possible primes constitute exactly one third of allo integers.
By modulation (modulo 9) possible primes have modules II,V,VIII,or
I,IV,VII.

Y.s.

Troels Munkner

[xilman]

Originally Posted by troels munkner

a polite dialogue will be appreciated
All integers from - infinity to + infinity can be subdivided into three groups.
A. Even integers which will be products of 2 and an other integer.
B. Odd integers divisible by 3 which will be products of 3 and an other
odd integer.
C. Odd integers which are not divisible by 3.
Their general form is (6*m +1), m being an integer from - infinity
to + infinity.
These integers can be grouped as "possible primes" and comprise
real primes and possible prime products.
All possible primes are "located" along a straight line wuith an individual
difference of 6, i.e. (6*m +1) --- (-35), (-29), (-23), (-17), (-11), (-5),
1,7,13,19,25,31,37 --- (6*m +1)
Possible primes constitute exactly one third of allo integers.
By modulation (modulo 9) possible primes have modules II,V,VIII,or
I,IV,VII.

Y.s.

Troels Munkner

This statement is both correct and trivial. It also defines the term "possible prime" to mean integers of the form . No-one but you uses the term "possible prime" but that's ok.

Where you go seriously off the rails is your claim that neither 2 nor 3 is a prime number. By making this statement you are not using the word "prime" in the same sense as it is used by essentially all mathematicians.

Like Humpty Dumpty you are at liberty to use whatever words you wish with whatever meaning you choose to assign to them The downside of that freedom is that if you use words with a meaning different from that understood by everyone else, you can guarantee that no-one will understand you.

If your objective is to annoy others and/or make yourself look stupid --- fair enough, though we have the freedom to ridicule you and/or express our annoyance. On the other hand, if you wish to communicate your ideas it is a very good idea to use a common language and that includes using words which have mutually agreed meaning.


Paul

[S485122]

Originally Posted by troels munkner

a polite dialogue will be appreciated
All integers from - infinity to + infinity can be subdivided into three groups.
A. Even integers which will be products of 2 and an other integer.
B. Odd integers divisible by 3 which will be products of 3 and an other
odd integer.
C. Odd integers which are not divisible by 3.
Their general form is (6*m +1), m being an integer from - infinity
to + infinity.
These integers can be grouped as "possible primes" and comprise
real primes and possible prime products.
All possible primes are "located" along a straight line wuith an individual
difference of 6, i.e. (6*m +1) --- (-35), (-29), (-23), (-17), (-11), (-5),
1,7,13,19,25,31,37 --- (6*m +1)
Possible primes constitute exactly one third of allo integers.

If I understand well 5 is not an integer since it is not Even, not divisible by 3 and not of the form 6 * m + 1.

So all numbers of the form 6 * m + 5 (where m is an integer) are not integers.

I can deduce from that, that 31 for instance can not be an integer, and thus not be a "possible prime", since it would require m = 5 to get 6 * 5 + 1 = 31.

[R.D. Silverman]

Originally Posted by Jacob Visser

If I understand well 5 is not an integer since it is not Even, not divisible by 3 and not of the form 6 * m + 1.

So all numbers of the form 6 * m + 5 (where m is an integer) are not integers.

I can deduce from that, that 31 for instance can not be an integer, and thus not be a "possible prime", since it would require m = 5 to get 6 * 5 + 1 = 31.

Note that the integers that are 1 mod 6 form an algebra in which unique
multiplication FAILS. Take the number 3025. It is in the set. So are
25 (a prime), 121 (a prime) and 55 (a prime).

But 3025 = 25*121 (product of two primes)
= 55*55 (square of a different prime!)

So we have a number that is the square of a prime also equal to the
product of two different primes!

[mfgoode]

Originally Posted by xilman

This statement is both correct and trivial. It also defines the term "possible prime" to mean integers of the form . No-one but you uses the term "possible prime" but that's ok.

Where you go seriously off the rails is your claim that neither 2 nor 3 is a prime number. By making this statement you are not using the word "prime" in the same sense as it is used by essentially all mathematicians.
Paul

The only reason I can presume to explain this is that 1 is not considered a prime. It is its own square and this property is unique.

Since 2 is considered the only even prime it 'may' also be dropped out of the 'real' prime sequence.

Now Goldbach's conjecture is that every even number greater the two (2=1+1) is the sum of 2 prime numbers. So two is not, by definition above of 1, not being a prime and Goldbach makes 2 an exception to his rule..

Is that what you mean Troels?

But why do you consider 3 as not a prime number? Have you a logical reason?

Mally

[ewmayer]

Originally Posted by R.D. Silverman

Note that the integers that are 1 mod 6 form an algebra in which unique
multiplication FAILS. Take the number 3025. It is in the set. So are
25 (a prime), 121 (a prime) and 55 (a prime).

See, if the original poster used language more like that (or had anything meaningful to say), we might take him more seriously...